Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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What is a “note” (that might be published) in mathematics?

My background is not in mathematics but I am translating a novel from the French that has a few mathematicians as characters. A few times, the publication of a "note" is mentioned. This is the French ...
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1answer
31 views

Is there a concept called the cross derivative between two functions?

Let $f$ and $g$ be two real functions. Is there already a concept for the quantity $\lim_{h \to 0} \frac{f(x+h)-g(x)}{h}$? Note that when $g=f$, the quantity, if exists, is the derivative of $f$ at ...
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2answers
91 views

The phrase “up to”

I have begun seeing the phrase "up to" a lot after taking abstract algebra. I usually can figure out what means in context. For example, $\mathbb Z_4$ equals the set of rotations of a square, up to ...
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1answer
21 views

Jargon for maximum/minumum absolute value in a set

Given a group of numbers $-5,-3,1,2$, the maximum is 2, the minimum is -5. What is the mathematical jargon for the maximum and minimum in absolute terms (i.e. -5 and 1 respectively)? Basically, I ...
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3answers
94 views

G/N read as G modulo N.

In my abstract algebra course, the instructor is calling G/N (the set of left Cosets of N in G) G mod N. This has not yet been explained. Why is this the case? My immediate suspicion is some ...
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2answers
70 views

Name and role of a particular finite group?

The group generated by the functions $x\mapsto 1/x$ and $x\mapsto 1-x$ with composition of functions as the group operation is a non-abelian group with only six elements (listed below). Does this ...
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2answers
15 views

Correct term for percentage in decimal form

I have 35% of something, but when I calculate how much that is I multiply the total by 0.35 Is there a unambiguous word for the decimal form of a percent? "Decimal" is too broad because it can refer ...
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1answer
22 views

What's the name given to the ratio $P^2/A$ for a closed figure in the Euclidean plane?

Let $\mathscr{F}$ be the set of all plane, closed Euclidean figures having positive perimeter, and let $\sim$ be the similarity relation on $\mathscr{F}$. Then, for any equivalence class ...
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37 views

division algebras in Weil's Basic Number Theory

I have a question regarding the terminology in Weil's Basic Number Theory. In Corollary 5 of I-§4 (p. 14) there is a statement regarding division algebras over local fields. It starts like this: Let ...
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1answer
25 views

What is “Real coordinate space”?

What is the Real Coordinate Space in the discussion of vectors? How does it relate to Cartesian Coordinate System and Euclidean Space? P.S. Please, use naive terms.
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1answer
55 views

Name for a continuous surjection such that $\operatorname{cl}(f^{-1}(A)) = f^{-1}(A') \implies \operatorname{cl}(A) = A'$

Consider a continuous surjective map $f \colon (X, \tau) \to (X', \tau')$ satisfying $$\operatorname{cl}(f^{-1}(A)) = f^{-1}(A') \implies \operatorname{cl}(A) = A'$$ for all $A, A' \in \wp(X')$ I ...
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2answers
49 views

What is the general definition of a discriminant? (Not just the definition for polynomials)

For example, in regards to the second derivative test for a function of two variables, $D=f_{xx}f_{yy}-(f_{xy})^2$ is refered to as the "second derivative test discriminant." I know that D is the ...
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0answers
14 views

Is there a name for “scales” that are bounded? (e.g. “severity scales”)

I'm coding a piece of software that has to deal with many quantities and mappings of these quantities to a this is "10 out of 100 bad" scale. For example: a server response time of 200ms is 50/100 ...
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1answer
109 views

Why are some branches of mathematics called 'theory' and others not?

We say: graph theory , group theory, number theory , set theory, what is definition of theory? We also say abstract algebra, real analysis, but why we do not say abstract algebra theory or real ...
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3answers
27 views

What does it mean for an object to be “under” an operation?

In the book Roads to Infinity: The Mathematics of Truth and Proof, the author stated: For each n, one has the n-string braid group $B_n$, consisting of all the n-string braids under the braid ...
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1answer
19 views

What's the difference between wave equation in PDE form and wave equation in normal form?

What's the difference between "wave equation in partial derivative form" and "wave equation in y(x,t) form" ? Are they both same? And why "wave equation in in y(x,t) form" is the solution of "wave ...
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0answers
101 views

Why is the sheaf $\mathcal{O}_X(n)$ called the “twisting sheaf” (where $X=\operatorname{Proj}(S)$ for a graded ring $S$)?

Basically my question is why the sheaf $\mathcal{O}_X(n)$ is called the twisting sheaf, here $X=\operatorname{Proj}(S)$ and $S$ any graded ring.
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3answers
89 views

Explaining the meaning of equality

I've been tasked with explaining to a group of people what the notion of equality means in mathematics, I've come up with a working explanation, but would appreciate some input, suggestions etc. ...
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0answers
32 views

What are the numbers in an inequality called?

Summand is to addition what multiplicand is to multiplication, but what is the terminology for the quantities of an inequality, such as 1<4? My best guess is simply "quantity" for both parts of ...
3
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0answers
29 views

Technical name for an almost-monotonic function

I'm wondering if there’s a technical name or short phrase that describes a function that’s monotonic, subject to some uniformly bounded amount of backtracking. $\exists \epsilon \forall x , y : y \gt ...
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2answers
23 views

Name for plane perpendicular to a vector

In writing some vector processing requirements, I want to use the correct terminology. For a 3D vector defined between the origin and a point, is there a term or name for a plane that is perpendicular ...
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0answers
108 views

Is there a special name for functors from a category C to a subcategory of C?

Is there a special name for functors from a category $C$ to a subcategory $S$ of $C$ where $S \ne C$? I'm using $\ne$ pretty informally above. I'd be happy with anything that reasonably captures the ...
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0answers
39 views

Why do we call a linear mapping “linear mapping”? [migrated]

What are the historical reasons that created the term "linear mapping"?
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1answer
13 views

Like “time-inhomogeneous,” but for space

I'm talking about a random walk that is homogeneous in time but not in space--is there a term for this? I've searched for "space-inhomogeneous" but nothing came up. Thank you!
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1answer
42 views

Looking for a terminology in ring theory (“ideal” which is not necessarily closed under addition )

I am wondering if there is a name for the subsets $S$ of a commutative ring $R$ such that for every $r\in R$ and every $s\in S$ we have $rs\in S$. Thus $S$ is ...
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1answer
32 views

Existence of Partials Imply the Existence of Gradient Vector?

Let $f$ be a scalar function of three variables. Then the gradient vector is defined by: I read here that the existence of partial derivatives at some point $(x_0, y_0, z_0)$ does not imply the ...
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5answers
65 views

Is there any notation for general $n$-th root $r$ such that $r^n=x$?

As we know that the notation for the $n$-th principal root is $\sqrt[n]{x}$ or $x^{1/n}$. But the principal root is not always the only possible root, e.g. for even $n$ and positive $x$ the principal ...
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0answers
23 views

Mathematical formal expression of find “subfunction” in function [closed]

Imagine if I have a function $s(t)$ and $r(t)$. $s(t)$ may contain $r(t)$ one or more times as $s(t)$ is a quasi-period function. What is the correct expression if I want to say the $s(t)$ contains ...
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1answer
35 views

What is it called when you have two systems of measurement and each scale has two different numbers that can represent the same thing?

I'd like to know what it is called in Math when you have two numbering systems and they represent the same thing, but with different numbers. Let me give you an example, when you have civilian and ...
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1answer
77 views

Contracted version of “isomorphic”

Had a look around and I can't find a word which acts as a contraction for "isomorphic" in the same way that "monic/epic" is a contraction of "monomorphic/epimorphic". For some reason this strikes me ...
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34 views

What is the opposite of a derangement?

A derangement is a bijection $f : A \rightarrow A$ such that $f(x) \ne x$ for all $x \in A$. Is there a name for a bijection $f : A \rightarrow A$ that is not a derangement? That is, is there a name ...
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1answer
77 views

Which slope is greater: one going very slightly downward, or one going quite steeply downward?

I've been arguing back and forth with someone about this for a while now. It seems to me like a number closer to positive infinity is considered greater, no matter if you are talking about slopes or ...
3
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1answer
60 views

Isomorphic or equal?

Let $\sim_n$ be the usual equivalence relation of congruence modulo $n$ in $\mathbb{Z}$, i.e., for $a,b\in\mathbb{Z}$, $a\sim_nb\Leftrightarrow a-b=k\cdot n$ for some $k\in\mathbb{Z}$. For $n=0$ the ...
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1answer
30 views

How do you call a vector of length $n$, with all values equal to $\frac{1}{n}$?

Is there a specific name for a vector of dimension $n$, with all values equal to $\frac{1}{n}$? So, a vector that looks like this: $\vec{v} = \underbrace{(\frac{1}{n}, \frac{1}{n}, ..., \frac{1}{n}, ...
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1answer
36 views

How to mathematically state y - 1 unless y - 1 < 0 then y is 0

I have a formula and I don't know how to write it in mathematical form (I'm a programmer.) The formula needs the variable y to be y - 1 unless y <= 0, in which case y should just be 0. ...
2
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0answers
23 views

Name of the segment connecting a point's coordinate axis projections?

Given any point $(x,y)$ in the real plane consider the corresponding line segment connecting $(x,0)$ with $(0,y)$. See diagram. Is there a name for this special segment? (I believe that in ...
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1answer
41 views

What's the name of this type of a set?

So I have a set $\{i_1,i_3,i_5\}$. What do we call the following set? Is there a standard name for it? $\emptyset, \{i_1\}, \{i_1,i_3\}, \{i_1,i_3,i_5\}$. Note that we do not have $\{i_3,i_5\}$ in it ...
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1answer
18 views

Terminology: Expected Value, Expectation, Expectation Value

According to [Wikipedia::Expected Value] expected value and expectation are correct terms for the first moment of a random variable. What about expectation value? I have heard and read this term ...
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1answer
22 views

What is the difference between functions and operations?

Wikipedia says that an operation $\omega$ is a function of the form $\omega: V \to Y$, where $V \subset X_1 \times\cdots\times X_k$. But as far as I know, every function's domain is a set, so ...
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173 views

What is known about these arithmetical functions?

Let $n=\prod_p p^{c_p}$, $N\in \mathbb N$ and $$ \alpha_N(n)=\prod_p p^{c_p \bmod N}. $$ The function $\alpha_N$ is multiplicative since $\alpha_N(n)\alpha_N(m)=\alpha_N(nm)$ for co-prime $n$ and $m$ ...
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2answers
77 views

Is 'clamp' a formally recognized mathematical function?

I was surprised to find the clamp function absent from Mathworld and Wikipedia. Is this mainly a concept particular to computer programming? Is it known by another ...
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0answers
15 views

mathematical name for the relationship between capacity utilization and overcapacity

I'm writing a report on industrial overcapacity, which is capacity not utilized by current production. If capacity utilization is the percent of total capacity utilized, what is the mathematical name ...
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2answers
129 views

What are the formal terms for the intersection points of the geometric representation of the extended trigonometric functions?

Mike Pierce's answer to this question, regarding trigonometric functions beyond the common (co)sine, (co)secant, and (co)tangent, points to a figure on the Wikipedia page on trigonometric functions ...
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1answer
39 views

Graph vertex set with a certain property

Let $G$ be a graph and let $V$ be a set of vertices with the following property: If a vertex $v$ is connected to every $u\in V$, then $v$ has to be in $V$. Does such $V$ have a (standard) name? Note ...
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2answers
427 views

Why we use the word 'compact' for compact spaces?

Considering the definition of compactness in either Analysis or Topology books, or its equivalent definitions (i.e. [It] is compact $\Longleftrightarrow\dots$), I couldn't understand why ...
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1answer
37 views

What do the letters a, b and c stand for in linear programming?

From the definition of linear programming: ...
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1answer
53 views

Right modules Vs Left modules.

I have been reading Frobenius Algebras, Volume 1 By Andrzej Skowroński, Kunio Yamagata. On page 18 I came across the following paragraph, and I founded interesting, I will quote it and then ask my ...
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4answers
78 views

What is $\sqrt{(-1)^2}$ [duplicate]

This question is primarily terminology based. In that $\sqrt{}$ denotes the principal square root. Here are two reasoning $\sqrt{(-1)^2}=1$ since $\sqrt{(-1)^2}=\sqrt{1}$ which we know has a ...
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0answers
37 views

Given bifunctor $F$, what is the name of the functor with switched arguments?

Sorry for the unspecific title. Here the actual question: Given categories $\mathcal{A},\mathcal{B}$, let $S$ be the canonical functor $\mathcal{B} \times \mathcal{A} \to \mathcal{A} \times ...
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2answers
39 views

Terminology: The difference between $X$'s convention

I am reading the paper, Classification in Networked Data: A Toolkit and a Univariate Case Study. And I have a question about the terminology of this paper, on page 938: Also, see the following ...